As a participant in your school's community service project, you volunteer a total of 40 hours over the course of the school year. Your volunteer hours include serving at a soup kitchen, picking up trash at several local parks, and collecting toys for needy children. You spend 4 times as many hours collecting toys as picking up trash, and 2 hours less serving at the soup kitchen than picking up trash.

Solve this system of equations using Cramer's Rule.

December 30th 2008, 04:24 AM

HallsofIvy

Quote:

Originally Posted by magentarita

As a participant in your school's community service project, you volunteer a total of 40 hours over the course of the school year. Your volunteer hours include serving at a soup kitchen, picking up trash at several local parks, and collecting toys for needy children. You spend 4 times as many hours collecting toys as picking up trash, and 2 hours less serving at the soup kitchen than picking up trash.

Solve this system of equations using Cramer's Rule.

First, of course, you need a system of equations! (In fact, in my opinion, that's a badly stated problem. What you are really asked to do is find how many hours you spend doing each of three different kinds of things You shouldn't be asked to "solve the system of equation" when no system of equations has been given!). Let "s" be the number of hours you spend serving at the soup kitchen, "p" be the number of hours you spend picking up trash, and "c" be the number of hours you spend collecting toys.

Now translate each sentence into an equation:
" you volunteer a total of 40 hours" s+ p+ c= 40.

"You spend 4 times as many hours collecting toys as picking up trash"
c= 4p.

Now, Cramer's rule says that the solution can be written s= u/d, p= v/d, and c= w/d where d is the determinant formed from the coefficients and u, v, w are the same determinant but with the first, second, and third columns, respectively, replaced by the numbers on the right hand side of the equations.
That is

Can you find those determinants by yourself?

December 30th 2008, 09:58 PM

magentarita

yes...

Quote:

Originally Posted by HallsofIvy

First, of course, you need a system of equations! (In fact, in my opinion, that's a badly stated problem. What you are really asked to do is find how many hours you spend doing each of three different kinds of things You shouldn't be asked to "solve the system of equation" when no system of equations has been given!). Let "s" be the number of hours you spend serving at the soup kitchen, "p" be the number of hours you spend picking up trash, and "c" be the number of hours you spend collecting toys.

Now translate each sentence into an equation:
" you volunteer a total of 40 hours" s+ p+ c= 40.

"You spend 4 times as many hours collecting toys as picking up trash"
c= 4p.

Now, Cramer's rule says that the solution can be written s= u/d, p= v/d, and c= w/d where d is the determinant formed from the coefficients and u, v, w are the same determinant but with the first, second, and third columns, respectively, replaced by the numbers on the right hand side of the equations.
That is

Can you find those determinants by yourself?

Yes, I can find the determinants. I'll do that on my next day off.

December 31st 2008, 05:56 AM

HallsofIvy

I do problems like that while my boss isn't looking!(Rofl)

January 1st 2009, 01:29 PM

magentarita

me too...

Quote:

Originally Posted by HallsofIvy

I do problems like that while my boss isn't looking!(Rofl)

Believe it or not, I take math sheets to work and work out math questions in the bathroom and on my lunch break. I want to master this stuff.

January 1st 2009, 01:33 PM

janvdl

Quote:

Originally Posted by magentarita

Believe it or not, I take math sheets to work and work out math questions in the bathroom and on my lunch break. I want to master this stuff.